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40-501: The foundation of the unitary group approach (UGA) can be traced to the work of Moshinsky. Later, Shavitt introduced the graphical aspect (GUGA) drawing on the earlier work of Paldus. Computer programs based on the GUGA method have been shown to be highly efficient. offering certain performance advantages over the older, sometimes called traditional, techniques for CSF construction. However traditional methods can offer other advantages such as

80-630: A consortium which worked on the key problems of the day, such as atomic and molecular structure, and exchanged both scientific information and personnel in their scientific quests. These institutes were located at the LMU, under Arnold Sommerfeld , the University of Göttingen, under Max Born , and the University of Copenhagen , under Niels Bohr . Furthermore, Werner Heisenberg and Born had just recently published their trilogy of papers which launched

120-401: A few characteristics of the potential surface. Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surfaces (corresponding to different electronic quantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by Stueckelberg , Landau , and Zener in the 1930s, in their work on what

160-480: A prominent theme in Heitler's career. While Heitler was at Göttingen, Adolf Hitler came to power in 1933. With the rising prominence of anti-Semitism under Hitler, Born took it upon himself to take the younger Jewish generation under his wing. In doing so, Born arranged for Heitler to get a position that year as a Research Fellow at the University of Bristol , with Nevill Francis Mott . At Bristol, Heitler

200-530: A way which could be followed by chemists. The text soon became a standard text at many universities. In 1937, Hans Hellmann appears to have been the first to publish a book on quantum chemistry, in the Russian and German languages. In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding. In addition to the investigators mentioned above, important progress and critical contributions were made in

240-421: Is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics . Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy , nuclear magnetic resonance (NMR) spectroscopy , and scanning probe microscopy . Quantum chemistry may be applied to

280-558: Is now known as the Landau–Zener transition . Their formula allows the transition probability between two adiabatic potential curves in the neighborhood of an avoided crossing to be calculated. Spin-forbidden reactions are one type of non-adiabatic reactions where at least one change in spin state occurs when progressing from reactant to product . Walter Heitler Walter Heinrich Heitler FRS MRIA German: [ˈhaɪtlɐ] ; 2 January 1904 – 15 November 1981)

320-524: Is the Born–Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKM theory in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable simple estimates of unimolecular reaction rates from

360-520: The Feynman path integral formulation to add quantum corrections to molecular dynamics, which is called path integral molecular dynamics . Statistical approaches, using for example classical and quantum Monte Carlo methods , are also possible and are particularly useful for describing equilibrium distributions of states. In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy surfaces . This

400-468: The Schrödinger equation is a central goal of quantum chemistry. Progress in the field depends on overcoming several challenges, including the need to increase the accuracy of the results for small molecular systems, and to also increase the size of large molecules that can be realistically subjected to computation, which is limited by scaling considerations — the computation time increases as a power of

440-477: The University of Zurich . He then became an assistant to Max Born at the Institute for Theoretical Physics at the University of Göttingen . Heitler completed his Habilitation , under Born, in 1929, and then remained as a Privatdozent until 1933. In that year, he was let go by the university because he was Jewish. At the time Heitler received his doctorate, three Institutes for Theoretical Physics formed

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480-535: The electronic molecular Hamiltonian , usually making use of the Born–Oppenheimer (B–O) approximation. This is called determining the electronic structure of the molecule. An exact solution for the non-relativistic Schrödinger equation can only be obtained for the hydrogen atom (though exact solutions for the bound state energies of the hydrogen molecular ion within the B-O approximation have been identified in terms of

520-430: The generalized Lambert W function ). Since all other atomic and molecular systems involve the motions of three or more "particles", their Schrödinger equations cannot be solved analytically and so approximate and/or computational solutions must be sought. The process of seeking computational solutions to these problems is part of the field known as computational chemistry . As mentioned above, Heitler and London's method

560-561: The matrix mechanics formulation of quantum mechanics . Also, in early 1926, Erwin Schrödinger, at the University of Zurich , began to publish his quintet of papers which launched the wave mechanics formulation of quantum mechanics and showed that the wave mechanics and matrix mechanics formulations were equivalent. These papers immediately put the personnel at the leading theoretical physics institutes onto applying these new tools to understanding atomic and molecular structure. It

600-737: The 1942–1943 academic year, Heitler gave a course on elementary wave mechanics, during which W. S. E. Hickson took notes and prepared a finished copy. These notes were the basis for Heitler's book Elementary Wave Mechanics: Introductory Course of Lectures , first published in 1943. A new edition was published as Elementary Wave Mechanics in 1945. This version was revised and republished many times, as well as being translated into French and Italian and published in 1949 and in German in 1961. A further revised version appeared as Elementary Wave Mechanics With Applications to Quantum Chemistry in 1956, as well as in German in 1961. Schrödinger resigned as Director of

640-525: The Coulomb field of an atomic nucleus, in which they developed the Bethe-Heitler formula for Bremsstrahlung . In 1936, Heitler published his major work on quantum electrodynamics, The Quantum Theory of Radiation , which marked the direction for future developments in quantum theory. The book appeared in many editions and printings and has been translated into Russian. Heitler also contributed to

680-533: The School for Theoretical Physics in 1946, but stayed at Dublin, whereupon Heitler became Director. Heitler stayed at Dublin until 1949, when he accepted a position as Ordinarius Professor for Theoretical Physics and Director of the Institute for Theoretical Physics at the University of Zurich , where he remained until 1974, when he retired. In 1958, Heitler held the Lorentz Chair for Theoretical Physics at

720-473: The ability to handle degenerate symmetry point groups, such as C ∞ v {\displaystyle C_{\infty v}} . This quantum chemistry -related article is a stub . You can help Misplaced Pages by expanding it . Quantum chemistry Quantum chemistry , also called molecular quantum mechanics , is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards

760-483: The density functional is split into four terms; the Kohn–Sham kinetic energy, an external potential, exchange and correlation energies. A large part of the focus on developing DFT is on improving the exchange and correlation terms. Though this method is less developed than post Hartree–Fock methods, its significantly lower computational requirements (scaling typically no worse than n with respect to n basis functions, for

800-485: The early years of this field by Irving Langmuir , Robert S. Mulliken , Max Born , J. Robert Oppenheimer , Hans Hellmann , Maria Goeppert Mayer , Erich Hückel , Douglas Hartree , John Lennard-Jones , and Vladimir Fock . The electronic structure of an atom or molecule is the quantum state of its electrons. The first step in solving a quantum chemical problem is usually solving the Schrödinger equation (or Dirac equation in relativistic quantum chemistry ) with

840-444: The electronic wave function is adiabatically parameterized by the nuclear positions (i.e., the Born–Oppenheimer approximation ). A wide variety of approaches are used, including semi-empirical methods, density functional theory , Hartree–Fock calculations, quantum Monte Carlo methods, and coupled cluster methods. Understanding electronic structure and molecular dynamics through the development of computational solutions to

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880-620: The first step of his path to the 1950 Nobel Prize in Physics, "for his development of the photographic method of studying nuclear processes and his discoveries regarding mesons made with this method". After the fall of France in 1940, Heitler was briefly interned on the Isle of Man for several months. Heitler remained at Bristol eight years, until 1941, when he became a professor at the Dublin Institute for Advanced Studies , which

920-514: The hydrogen molecule. Their valence bond treatment of this problem, was a landmark in that it brought chemistry under quantum mechanics. Furthermore, their work greatly influenced chemistry through Linus Pauling , who had just received his doctorate and on a Guggenheim Fellowship visited Heitler and London in Zurich. Pauling spent much of his career studying the nature of the chemical bond. The application of quantum mechanics to chemistry would be

960-547: The method appeared so straightforward that 'even a theoretician might be able also to do it'. This intrigued Powell, and he convinced theoretician Heitler to travel to Switzerland with a batch of llford emulsions and expose them on the Jungfraujoch at 3500m. In a letter to 'Nature' in August 1939, Heitler and Powell were able to confirm the observations of Blau and Wambacher. Thus Heitler had some influence in setting Powell on

1000-429: The motion of molecules. Direct solution of the Schrödinger equation is called quantum dynamics , whereas its solution within the semiclassical approximation is called semiclassical dynamics. Purely classical simulations of molecular motion are referred to as molecular dynamics (MD) . Another approach to dynamics is a hybrid framework known as mixed quantum-classical dynamics ; yet another hybrid framework uses

1040-424: The number of atoms. Some view the birth of quantum chemistry as starting with the discovery of the Schrödinger equation and its application to the hydrogen atom. However, a 1927 article of Walter Heitler (1904–1981) and Fritz London is often recognized as the first milestone in the history of quantum chemistry. This was the first application of quantum mechanics to the diatomic hydrogen molecule , and thus to

1080-516: The phenomenon of the chemical bond. However, prior to this a critical conceptual framework was provided by Gilbert N. Lewis in his 1916 paper The Atom and the Molecule , wherein Lewis developed the first working model of valence electrons . Important contributions were also made by Yoshikatsu Sugiura and S.C. Wang. A series of articles by Linus Pauling , written throughout the 1930s, integrated

1120-408: The prediction and verification of spectroscopic data as well as other experimental data. Many quantum chemistry studies are focused on the electronic ground state and excited states of individual atoms and molecules as well as the study of reaction pathways and transition states that occur during chemical reactions . Spectroscopic properties may also be predicted. Typically, such studies assume

1160-409: The pure functionals) allow it to tackle larger polyatomic molecules and even macromolecules . This computational affordability and often comparable accuracy to MP2 and CCSD(T) (post-Hartree–Fock methods) has made it one of the most popular methods in computational chemistry . A further step can consist of solving the Schrödinger equation with the total molecular Hamiltonian in order to study

1200-503: The quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules , materials , and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry

1240-480: The understanding of cosmic rays, as well as predicted the existence of the electrically neutral pi meson. While developing the theory of cosmic ray showers in 1937, he became aware of the latest experimental work in the field: the observation of cosmic ray interactions in Nuclear emulsion by Austrian physicists Marietta Blau and Hertha Wambacher . He mentioned this to Bristol colleague Cecil Powell , saying that

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1280-616: The work of Heitler, London, Sugiura, Wang, Lewis, and John C. Slater on the concept of valence and its quantum-mechanical basis into a new theoretical framework. Many chemists were introduced to the field of quantum chemistry by Pauling's 1939 text The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry , wherein he summarized this work (referred to widely now as valence bond theory ) and explained quantum mechanics in

1320-719: Was a German physicist who made contributions to quantum electrodynamics and quantum field theory . He brought chemistry under quantum mechanics through his theory of valence bonding . In 1922, Heitler began his study of physics at the Karlsruhe Technische Hochschule , in 1923 at the Humboldt University of Berlin , and in 1924 at the Ludwig Maximilian University of Munich (LMU), where he studied under both Arnold Sommerfeld and Karl Herzfeld . The latter

1360-508: Was a Research Fellow of the Academic Assistance Council, in the H. H. Wills Physics Laboratory. At Bristol, among other things, he worked on quantum field theory and quantum electrodynamics on his own, as well as in collaboration with other scientific refugees from Hitler, such as Hans Bethe and Herbert Fröhlich , who also left Germany in 1933. With Bethe, he published a paper on pair production of gamma rays in

1400-543: Was arranged there by Erwin Schrödinger, Director of the School for Theoretical Physics. He has been described as the "unsung hero of DIAS in the 1940s". At Dublin, Heitler's work with H. W. Peng on radiation damping theory and the meson scattering process resulted in the Heitler-Peng integral equation. During his stay in Dublin he lived at 21 Seapark Road, Clontarf, down the road from Erwin Schrödinger. During

1440-589: Was developed in 1929 by Friedrich Hund and Robert S. Mulliken , in which electrons are described by mathematical functions delocalized over an entire molecule . The Hund–Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic properties better than the VB method. This approach is the conceptual basis of the Hartree–Fock method and further post-Hartree–Fock methods. The Thomas–Fermi model

1480-453: Was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of electronic density instead of wave functions , although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory (DFT). Modern day DFT uses the Kohn–Sham method , where

1520-504: Was extended by Slater and Pauling to become the valence-bond (VB) method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds . It focuses on how the atomic orbitals of an atom combine to give individual chemical bonds when a molecule is formed, incorporating the two key concepts of orbital hybridization and resonance . An alternative approach to valence bond theory

1560-469: Was his thesis advisor when he obtained his doctorate in 1926; Herzfeld taught courses in theoretical physics and one in physical chemistry, and in Sommerfeld's absence often took over his classes. From 1926 to 1927, he was a Rockefeller Foundation Fellow for postgraduate research with Niels Bohr at the Institute for Theoretical Physics at the University of Copenhagen and with Erwin Schrödinger at

1600-591: Was in this environment that Heitler went on his Rockefeller Foundations Fellowship, leaving LMU and within a period of two years going to do research and study with the leading figures of the day in theoretical physics, Bohr's personnel in Copenhagen, Schrödinger in Zurich, and Born in Göttingen. In Zurich, with Fritz London , Heitler applied the new quantum mechanics to deal with the saturable, nondynamic forces of attraction and repulsion, i.e., exchange forces, of

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